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Width and finite
extinction time of Ricci flow
Tobias H Colding and William P Minicozzi II |
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Geometry & Topology 12 (2008) 2537–2586
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Abstract |
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This is an expository article with complete proofs intended for a general nonspecialist audience. The results are two-fold. First, we discuss a geometric invariant, that we call the width, of a manifold and show how it can be realized as the sum of areas of minimal –spheres. For instance, when is a homotopy –sphere, the width is loosely speaking the area of the smallest –sphere needed to ‘pull over’ . Second, we use this to conclude that Hamilton’s Ricci flow becomes extinct in finite time on any homotopy –sphere. |
Keywords
width, sweepout, min-max, Ricci flow, extinction, harmonic
map, bubble convergence
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Mathematical Subject Classification 2000
Primary: 53C44, 53C42
Secondary: 58E12, 58E20
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References |
Publication
Received: 30 June 2007
Accepted: 10 October 2008
Published: 6 November 2008
Proposed: Ben Chow
Seconded: Colin Rourke, Martin Bridson
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Authors |
| Tobias H Colding | |
| Department of Mathematics, MIT 77 Massachusetts Avenue Cambridge, MA 02139-4307, USA and Courant Institute of Mathematical Sciences 251 Mercer Street New York, NY 10012 USA |
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| William P Minicozzi II | |
| Department of Mathematics Johns Hopkins University 3400 N Charles St Baltimore, MD 21218 USA |
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